We demonstrate how a single scanning voltage probe can be used to map the local conductivity and current density in a thin film with no a priori knowledge of the geometry of the electrical contacts. With state-of-the-art scanning voltage probes, under appropriate conditions such mapping should be possible down to nanometer scales. The technique requires two non-colinear voltage scans. When only one voltage map is available, determination of the conductivity is not possible because the solution to the governing equation is not unique. The only restriction on the technique is that the sheet conductivity is a local function of position.
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